I was just going to ask the very same thing.
They usually announce rulings a 10 AM EST by posting them on their website.
From their site:
Today at the Court - Monday, Mar 4, 2024
The Supreme Court Building is open to the public from 9 a.m. to 3 p.m.
The Court will release an order list at 9:30 a.m.
The Court may announce opinions on the homepage beginning at 10 a.m. The Court will not take the Bench.
Courtroom Lectures available within the next 30 days.